SOLUTION: What are the following triangles with these lengths for sides? Are they right triangles, acute triangles, or obtuse triangles? 3, 4, 5 5, 8, 10 3, 4, 6 3, 5, 8 4, 5, 8 4, 5

Algebra.Com
Question 573849: What are the following triangles with these lengths for sides? Are they right triangles, acute triangles, or obtuse triangles?
3, 4, 5
5, 8, 10
3, 4, 6
3, 5, 8
4, 5, 8
4, 5, 10
6, 8, 10

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


First check to see if you have a triangle at all. Add the two short dimensions. If the sum is STRICTLY GREATER THAN the long side, then you have a triangle and you can proceed. (If the sum of the two short sides is equal to the third side, then you have a straight line -- not a triangle. If the sum of the two short sides is less than the third side, then you have two short sides flapping around unable to meet in a third vertex.)

Square the measures of each of the sides and then sum the squares of the two short sides.

If the sum is equal to the square of the long side, then you have a right triangle.

If the sum is less than the square of the long side, then you have an obtuse triangle.

If the sum is greater than the square of the long side, then you have an acute triangle.

Example: 3, 4, 6: 3 + 4 = 7 > 6, hence a triangle. 3 squared is 9, 4 squared is 16. 9 plus 16 is less than 6 squared (36), so you have an obtuse triangle.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism


RELATED QUESTIONS

Determine if the following sides could construct a triangle. If so, classify them as... (answered by greenestamps,Shin123)
Are the following triangles acute, right, obtuse, or not possible? 1. ^1, ^2, ^3 2. (answered by Alan3354,richwmiller)
Fundamental Ideas Points, Lines, and Planes Postulates and Theorems Segments,... (answered by richard1234)
Assume you are given two right triangles with congruent hypotenuses and wish to show that (answered by solver91311)
Sam is studying isosceles triangles. He wants to know how many isosceles triangles exist... (answered by edjones,richwmiller,Edwin McCravy)
use the converse of the pythagorean theroem to classify the triangles as acute, right, or (answered by Fombitz)
If all of the following triangles have the same perimeter, which has the greatest area? (answered by stanbon)
In each of the following answer true or false. Justify your reasons. (a) Congruent... (answered by Theo)
I need some help with this please. This is what the problem says: The following... (answered by Tatiana_Stebko)